Generalized inverses of matrices over commutative rings

K. Manjunatha Prasad

doi:10.1016/0024-3795(94)90081-7

Generalized inverses of matrices over commutative rings

K. Manjunatha Prasad^*

^*Corresponding author for this work

Department of Applied Statistics and Data Science, Prasanna School of Public Health, Manipal

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

A Rao-regular matrix and the Rao idempotent of a matrix over a commutative ring are defined. We prove that a matrix A over a commutative ring is regular if and only if A is a sum of Rao-regular matrices with mutually orthogonal Rao idempotents. We find necessary and sufficient conditions for a matrix to have group inverse over a commutative ring. Also, we give a method for computing minors of reflexive g-inverse whenever it exists.

Original language	English
Pages (from-to)	35-52
Number of pages	18
Journal	Linear Algebra and Its Applications
Volume	211
Issue number	C
DOIs	https://doi.org/10.1016/0024-3795(94)90081-7
Publication status	Published - 01-11-1994

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis

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10.1016/0024-3795(94)90081-7

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N2 - A Rao-regular matrix and the Rao idempotent of a matrix over a commutative ring are defined. We prove that a matrix A over a commutative ring is regular if and only if A is a sum of Rao-regular matrices with mutually orthogonal Rao idempotents. We find necessary and sufficient conditions for a matrix to have group inverse over a commutative ring. Also, we give a method for computing minors of reflexive g-inverse whenever it exists.

AB - A Rao-regular matrix and the Rao idempotent of a matrix over a commutative ring are defined. We prove that a matrix A over a commutative ring is regular if and only if A is a sum of Rao-regular matrices with mutually orthogonal Rao idempotents. We find necessary and sufficient conditions for a matrix to have group inverse over a commutative ring. Also, we give a method for computing minors of reflexive g-inverse whenever it exists.

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UR - https://www.scopus.com/pages/publications/0038836526#tab=citedBy

U2 - 10.1016/0024-3795(94)90081-7

DO - 10.1016/0024-3795(94)90081-7

M3 - Article

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EP - 52

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - C

ER -

Generalized inverses of matrices over commutative rings

Abstract

All Science Journal Classification (ASJC) codes

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